Distributed weighted vertex cover via maximal matchings

Abstract

In this paper we consider the problem of computing a minimum-weight vertex-cover in an n-node, weighted, undirected graph G = (V, E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(logn + log Ŵ) communication rounds, where Ŵ is the average vertex-weight. The previous best algorithm for this problem requires O(log n(log n + log Ŵ)) rounds and it is not fully distributed. For a maximal matching M in G it is a well-known fact that any vertex-cover in G needs to have at least |M| vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting. © Springer-Verlag Berlin Heidelberg 2005.